Over the next few years, the Von Bothmers discovered severed branches and other signs that their four tallest trees, including an approximately 80-year-old acacia, were being "topped," or cut indiscriminately without permission, says Garth Drozin, another attorney for the Von Bothmers.

The tabloid, the most profitable newspaper in Murdoch's portfolio, was shut in July amid an escalating investigation into illegal phone hacking at the company that has cast doubt on the 80-year-old Murdoch's succession plans.